If the gravitational constant `G`, Plank's constant `h` and speed of light `c` be chosen as basic units, find the dimension of mass.
Dimensional formulae: `G : M^(-1) L^(3) T^(-2), h ML^(2) T^(-1)`

Explanation

`m prop G^(a) h^(b) c^(c )`
`M prop [M^(-1) L^(3) T^(-2)]^(a) [ML^(2) T^(-1)]^(b) [LT^(-1)]^(c )`
`M^(1) L^(0) T^(0) prop M^(a + 2B + c) T^(2a - B - c)`
Comparing power of `M, L` and `T`
`- a + B = 1`
`3 a + 2 b + c = 0`
`- 2a - b - c = 0 `
Adding (ii) and (iii) `implies a + b = 0`
Adding (i) and (iv) `implies b = (1)/(2), a = - (1)/(2), c = (1)/(2)`